Abstract

Quantum computers will be able solve important problems with significant polynomial and exponential speedups over their classical counterparts, for instance in option pricing in finance, and in real-space molecular chemistry simulations. However, key applications can only achieve their potential speedup if their inputs are prepared efficiently. We effectively solve the important problem of efficiently preparing quantum states following arbitrary continuous (as well as more general) functions with complexity logarithmic in the desired resolution, and with rigorous error bounds. This is enabled by the development of a fundamental subroutine based off of the simulation of rank-1 projectors. Combined with diverse techniques from quantum information processing, this subroutine enables us to present a broad set of tools for solving practical tasks, such as state preparation, numerical integration of Lipschitz continuous functions, and superior sampling from probability density functions. As a result, our work has significant implications in a wide range of applications, for instance in financial forecasting, and in quantum simulation.

https://scirate.com/arxiv/2205.00519

Biography

Arthur is a PhD student at the University of Oxford studying the theory of quantum algorithms. He is the recipient of the 2021-2022 JPMorgan Chase FLARE PhD Research Fellowship, and has previously interned at both JPMorgan Chase and IBM Research.

Bálint is an internationally recognised quantum theorist whose research covers both practical and more fundamental aspects of quantum physics. He is currently a Glasstone Research Fellow at the University of Oxford.

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